How do ethnocentrism and discrimination relate to one another? Is it possible to be ethnocentric but not engage in discrimination?

To discriminate means to be prejudiced and bigoted and to treat people differently and unfairly based on their gender, age, race, culture, sexual orientation, and other social and biological concepts that define our identity. To be ethnocentric means to feel superior to other races and cultures and believe that your own ethnicity, tradition, culture, and customs are much better and much more valuable in comparison to other races and ethnic groups. As sociological phenomena, the terms discrimination and ethnocentrism may have somewhat different definitions, but they are also very closely related to one another. In fact, one can fuel the other and vice versa; discrimination can make you ethnocentric, and ethnocentrism can cause discrimination and prejudice.
Ethnocentric people firmly believe that their ethnic group is the best ethnic group in existence, and all other groups are inferior to them. Some say that, unlike discrimination, ethnocentrism can bring people together and unite them towards one idea or cause; however, this type of nationalism does not bring any good to the community or the group. In fact, when taken to its limits, ethnocentrism can cause great conflicts, wars, and even mass genocide. A lot of modern religious conflicts and disagreements today are, essentially, based on ethnocentrism.
Discrimination can cause violence as well, and it can greatly influence the way the society functions. A lot of studies show that prejudiced people are more inclined to discriminate against others, even though that is not always the case. It is noteworthy to mention, however, that no one is born a bigot or a discriminator. If the people in the community are ethnocentric, or if the child is born in a family which openly discriminates other people, then that child has the potential to grow up into a bigoted and prejudiced person.
Perhaps one of the key differences between ethnocentrism and discrimination is the fact that ethnocentrism generally revolves around ethnicity, culture, race, and nationality, while discrimination can include prejudice towards all of these social and biological concepts, but it can also mean prejudice and judgment based on sexual orientation, gender identity, religion, height, weight, age, socio-economic status, and mental and physical disability. Thus, to answer your second question, I believe that you can, in fact, be discriminatory towards other people without being ethnocentric, but I don't think that you could be ethnocentric without being discriminatory towards people who don't belong in your ethnic group.